456640800 has 432 divisors, whose sum is σ = 1891566432. Its totient is φ = 94617600.

The previous prime is 456640799. The next prime is 456640817. The reversal of 456640800 is 8046654.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (33).

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 1293424 + ... + 1293776.

It is an arithmetic number, because the mean of its divisors is an integer number (4378626).

Almost surely, 2^456640800 is an apocalyptic number.

456640800 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 456640800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (945783216).

456640800 is an abundant number, since it is smaller than the sum of its proper divisors (1434925632).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

456640800 is a wasteful number, since it uses less digits than its factorization.

456640800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 401 (or 381 counting only the distinct ones).

The product of its (nonzero) digits is 23040, while the sum is 33.

The square root of 456640800 is about 21369.1553412857. The cubic root of 456640800 is about 770.0606012910.

The spelling of 456640800 in words is "four hundred fifty-six million, six hundred forty thousand, eight hundred".